1/f structure of temporal fluctuation in rhythm performance and rhythmic coordination

This dissertation investigated the nature of pulse in the tempo fluctuation of music performance and how people entrain with these performed musical rhythms. In Experiment 1, one skilled pianist performed four compositions with natural tempo fluctuation. The changes in tempo showed long-range correlation and fractal (1/f) scaling for all four performances. To determine whether the finding of 1/f structure would generalize to other pianists, musical styles, and performance practices, fractal analyses were conducted on a large database of piano performances in Experiment 3. Analyses revealed signicant long-range serial correlations in 96% of the performances. Analysis showed that the degree of fractal structure depended on piece, suggesting that there is something in the composition's musical structure which causes pianists' tempo fluctuations to have a similar degree of fractal structure. Thus, musical tempo fluctuations exhibit long-range correlations and fractal scaling. To examine how people entrain to these temporal fluctuations, a series of behavioral experiments were conducted where subjects were asked to tap the pulse (beat) to temporally fluctuating stimuli. The stimuli for Experiment 2 were musical performances from Experiment 1, with mechanical versions serving as controls. Subjects entrained to all stimuli at two metrical levels, and predicted the tempo fluctuations observed in Experiment 1. Fractal analyses showed that the fractal structure of the stimuli was reected in the inter-tap intervals, suggesting a possible relationship between fractal tempo scaling, pulse perception, and entrainment. Experiments 4-7 investigated the extent to which people use long-range correlation and fractal scaling to predict tempo fluctuations in fluctuating rhythmic sequences.